Polar resolver

ABSTRACT

A polar resolver for developing analog voltage outputs corresponding to X and Y coordinate input data through the provision of divider-inverter means to develop suitable X, Y, and R (the vector of X and Y) function voltage outputs corresponding to progressive accretions of angle theta and applying such outputs to switching and summing amplifier means.

United States Patent 11 1' Manfred! 1 Apr. 30, 1974 POLAR RESOLVER3,584,783 6/1971 KObOii 235/186 x 3,671,731 6/1972 Denoncourt et a1...235/189 X [75] lnvenmr- Urbam M m 3,710,088 1/1973 Blaschke et a1235/186 x [73] Assignee: The United States of America as p representedby the Secretary of the Primary ExaminerJoseph F. Ruggiero Navy,Washington, DC. Attorney, Agent, or Firm-Richard S. Sciascia; J. W. [22]Filed: Apr. 23, 1973 Pease [21] Appl. No.: 353,272

[57] ABSTRACT 52 us. c1. 235/186, 235/189 A Polar resolver fordeveloping analog voltage Outputs 51 1111. c1 G06g 7/22 corresponding?to X and Y coordinate input data [58] Field f Search 2 5 1 189 7 5 2through they provision of divider-inverter means to de- 5 7 velopsuitable X, Y, and R (the vector of X and Y) function voitage outputscorresponding to progressive 5 References Cited accretions of angle 0and applying such outputs to UNITED STATES PATENTS switching and summingamplifier means. 3,482,086 12/1969 Case/e1] .Q 235/189 x I 2 Claims, 4Drawing Figures 5 POLAR RESOLVER BACKGROUND OF THE INVENTION DESCRIPTIONOF THE EMBODIMENT This invention is in the field of angle conversionand- 5 Problem of Obtaining P transformation Without /or generationapparatus and in a more limited sense to such apparatus utilizing anoutput voltage proportional to an angle.

In the past the normal procedure for obtaining analog voltagecorresponding to angular data has been through the utilization of sineand cosine functions. However, in the present state of electronicequipment art it is quite often feasible to obtain from electronicequipment output of voltages corresponding to X and Y components. Itwould be quite useful, therefore, in such equipment to provide a polarresolver for providing an analog voltage representative of the angle 6corresponding to any given X and Y coordinates as orthogonal components(two input signals) used to generate SUMMARY OF THE INVENTION A noveltyin the invention disclosed herein is the provision of electronic meansof relatively simple structure and cost which will respond to X and Yinputs to provide analog voltage outputs corresponding to specificassociated angles which are corrected for ambiguity factors to provide asatisfactorily accurate result and which do not utilize or require thesolving of trigonometric functions. In a preferred embodiment vectorsummer means, divider means and inverter means are provided to develop,responsive to X and Y input voltages, output voltages which arefucntions of X, Y and R, the latter being the vector of X and Y, eachfunction being representative of a specific range of angle 0. The aboveis combined with a switching and summing circuit means, responsive tothe output functions voltages, to provide a progressive angular summingfrom +O to +225 and from 0 to -225 while also making provision for usingone unconnected output of angle 0 voltage as a feedback to correct forpossible ambiguity and establish stabilization in critical angle areas.

DESCRIPTION OF THE DRAWINGS Other objects and many of the attendantadvantages of this invention will become readily appreciated as the samebecomes better understood by reference to the following detaileddescription when considered-in connection with the accompanying drawingswherein:

FIGS. 1, 2 and 3 are diagrammatic illustrations'of X, Y and Rrelationship and representative functions to progressively evaluate theangle 0 in both positiveand negative directions. I v

FIG. 4 is a diagram, partially in block and partially schematic, of anembodiment of the polar resolver of this invention. O

lizing trigonometric functions to thereby provide simplicity andlow-cost and is further directed to improvements which eliminateinstability and provide acceptable accuracy- In accomplishing the above,the approach adopted is one based upon the fact that the ratio of thearea of a sector of a circle is to the area of the circle as the sectorangle 0 is to 2 1r. Thus, in FIG. 1 the pie-shaped portion, OACB, of thecircle 10 is called a sector and bears a relationship to the area of thecircle 10 which corresponds to the relationship of 0 to 2 1r.

The area of the sector is conventionally obtained from the formula A, kR 0 sin 0). However, since we wish to avoid the complications ofcircuitry inv the several angular ranges.

mate area as /l., [(X+h)Y/2]. The coordinates X and Y, the vector radiusR and the X axis dimension, where X h R,being shown in FIG. 1., This isan approximate area of the sector because the calculation lacks thesegment ACB shownin shaded area in FIG. 1. This is the error portion andindicated as E; Using the formula A, [(X+ h)Y/ 2] where X+ h Rand thecircle area/1,, 11' R, then (A,/A,,) (0/21r) and simplifying, 0'(21rA,/A E 2' RY/21r R 5 (HR).

Thus, an approximate angle 0 can be obtained simply by dividing theinput signal Y by R which is the vector sum of the X and Y inputsignals.

The error being proportional to the difference in areas of the triangleOAB and the sector OACB, FIG. 1, which in turn is proportional to theangle 0, it is desirable to utilize small error areas and thereforesmall angles. One method of minimizing this error is by insertingdifferentvariables as a function of the angle 0 as in FIG. .2, When Y/Rbecomes greater than 45, the triange which would involve X/R must becomputed and subtracted from Thus, the circle when divided into summablesections becomes as shown in FIG. 2. Comparing the magnitudes of X/R andY/R will determine the switching points to be at +45 and :l35. At theseswitch points the correct biases and functions can be fed to andutilized in an amplifier to produce the desired angle 0. i

However, as shown in FIG. 3, it is preferred to allow the angle 0 to becumulative rather than to insert wholly new quantities as shown in FIG.2. We have then from-FIG. 3 the opportunity tosum positive angularaccretions in the ranges of +O to +45, +45 to +1 35 and +l35 to +225(l35) via the X Y functions respectively, Y/R, 45 X/R and 45 Y/R. In thenegative angular direction the ranges 0 to -45, 45 to 1 35, 1 35 to 225(+l35) may be summed via the X Y respective functions Y/R, X/R 45 and 45Electronic implementation of the diagram of FIG/3 in a circuit toreceiveX and Y voltage inputs corresponding to angles 0 and to transform orresolve the same into a correctedangle 0, is shown in FIG. 4. Thatportion of the circuit at the top of FIG. 4 of the drawing and involvinga vector summer 12, dividers l4 and 16, and inverters 18,. 20, 22 and24, is provided for development of the X 7 Y functions as set forth inFIG. 3 for nates X and Y areintroduced respectively via lines 26 and 28and via lines 30 and 32 as inputs to vector summer 12. Voltages X and Yare also passed as inputs to divider 14 by a line 34 and to divider 16by a line 36. Vector summer 12 provides the radius vector R voltage onits output line 38 and passes the voltage correspond ing to vector R asa second input to dividers l4 and 16 via lines 42 and 40. The output,X/R, of divider 14 is passed via lines 44 and 46 as one input toinverter 18. The other input to inverter 18 is via lines 48 and 50 froma 45- voltage source indicated, i.e., a voltage corresponding to theangle 45". The output then of inverter 18 is 45 X/R voltage which ispassed on lines 52 and 54 to inverter 20. The output Y/R of divider 16is fed on lines 56 and 58 as one input to inverter 22, the other inputthereto being from the 45 voltage source via lines 48 and 60. The outputof inverter 22 which is a voltage corresponding to 45 Y/R is fed bylines 62 and-64 as one input to inverter 24. A second input to inverter24 is obtained from the Y/R I output line 56 via a line 68 and amplifier70 set for a gain of 2 and a line 72.'The gain of 2 in amplifier 70 ascathodes of bridge diodes 116 and 118'are connected via line 120, aresistor 122 and a line 124 to a terminal 126 which acts as a source ofnegative voltage corresponding to 45". The functional input to bridge102 a second input to inverter 24, together with the input 45 Y/Rresults in an output on line 74 of a voltage corresponding to thefunction 45 Y/R. The input, 45 X/R, to inverter 20 results in an outputvoltage on line 76. corresponding to the function X/R' 45. The outputvoltage-corresponding to function X/R, of divider 14 is passed on lines44, 78 and 80 toinverter 19. The output of inverter 19 becomes thefunction X/R on line 82. We have then in accordance with the portion ofthe circuit of FIG. 4 thus far described provided the means forproviding the X, Y and R functions as required by FIG. 3 for progressivesummation of angles in the ranges of +0 to +225 and O to 225".

The remainder of the circuit of FIG. 4 comprises a voltage switching andsumming means responsive to the functional outputs of said divider. andinverter means described above to provide a summation analog voltagerepresentative to the angle 0 to which the X and Y voltage inputscorrespond..More particularly in the remainder of FIG. 4 there isprovided six diode clampby' lines 88 and 90 and responds to said outputto provide ambiguity resolving voltages as will be describedhereinaftetflhe output of summing amplifier 84 is also applied to anoperational amplifier 92 via line 88 and a line 94. The amplifier 92 isprovided with an adjustable attenuator feedbackmeans 96 connected bylines 98 and 100 from the output to the input of amplifier 92,

. for providing a scaled output of the desired analog volt agecorresponding to the angle 0;

Considering the six diode clamping circuits which form the switchingmeans mentioned above, clamping circuitsI and 4 include a diode bridge102 receiving a positive voltage input corresponding to +45 fromterminal 104 via line 106, resistor 108, and line connected'to theanodes of bridge diodes 112 and 114 as indicated. This input providesfor clamping at +45? voltage. To provide for clamping at 45 voltage, the

is the voltage Y/R obtained from the divider 16 via lines 56 and 128.The output of bridge 102 is passed via a line 130, resistor 132, and aline 134 to the summing amplifier 84. The first clamping circuit thusprovides a voltage input to the summing amplifier 84 which is thefunction of Y/R between +0 and 445, clamping at the voltagecorresponding to +45. The fourth clamping circuit performs the samefunction except that it clamps at 45 voltage and covers the range of Oto 45.

For the first and fourth clamping circuits described above and for theremainder of the clamping circuits to be described, it is necessary toprovide a positive and negative reference voltage source circuit andsuitable resistors as supply power sources for the overallswitchingcircuit. Suitable voltage values which have been used are and10 volts; With different resistors and 100 volts could also be used.Thus, as shown in FIG. 4, voltage from a positive reference voltagesource, terminal 136, is connected via line 138, a resistor 140, a line142, an output diode 144 and resistor 146 to lines148 and 134 leading tosumming amplifier 84. A negative reference voltage source, terminal 150is connected via lines 152 and 154, resistor 156, line 158, diode 160,resistor 1'62, and lines 164, 148 and 134 to the summation amplifier 84.

The second diode clamping circuit includes the resistor 140, diode 144and additional diodes 166 and 168. The anodes of diodes 144, 166 and 168are connected by lines 170, 172 and 174 as shown. The cathode side ofdiode 166 is connected by a line 176 to the output line of inverter 18to provide an input voltage corresponding to the function 45 X/R. Thecathode side of diode 168 is connected by a line 178 to terminal 180acting as a source of voltage corresponding to +90 as a clampingvoltage. The second circuit thus, as indicated in FIG. 3, covers theangular range of +45 to +135". l

The fifth diode clamping circuit includes the diode 160, resistor 156and two additional diodes 182 and 184 having their cathodes connected tothe cathode side of diode'160 via lines 186, 188, and 192, and

their anodes connected respectively by line 76 to the output ofinverter,- 20 to introduce the functional volt age X/R 45 and byline 194to terminal 196 as a source of 90 clamping voltages. The fifth. diodeclamping circuit then covers the range of 45 to -l 35 as shown in FIG.3.

The third diode clamping circuit comprises the diodes 198, 200,202 and204 and resistors 206 and 208. The positive reference source terminal136 is connected to the anode side of diodes 198,200, 202 and 204'vialines 138 and 139, resistor 206, and lines 210, 212, 214, 216,218, 220and 222. The cathode side of diode 198 connected to the summingamplifier via a line 224 and lines 148 and 134. The cathode side ofdiodes 200, 202 and 204 are connected respectively by line 82 to the X/Rfunction voltage of inverter 19, by a line 226 to the 45- Y/R' functionvoltage of inverter 22 and by lines 228 and230 to the 0 function outputof inverter 86. .The third diode clamping circuit thus covers the rangeof +1 35 to +225.. 1

The sixth diode clamping circuit comprises the diodes 232, 234, 236 and238, having their cathode sides connected together by lines 240, 242,244, 246, 248 and 250, together with the resistors 252 and 254.

The anode of diode 232 is connected via resistor 252 and lines 224, 148and 134 to the input side of summing amplifier 84. Negative referencepower is supplied to clamping circuit six from negative referenceterminal 150 via lines 152 and 256 to resistor 254. The functional inputX/R is supplied to the anode side of diode 234 from divider 14 via lines78 and 258. The functional input Y/R 45 is applied to the anode of diode236 from inverter 24 via line 74. The input functions in the sixthclamping circuit provide for a voltage output covering the angular rangeof 1 35 to 225. To eliminate any ambiguity which may exist betweenpositive and negative angles, the angle on input from inverter 86 of thevoltage corresponding to 0,, a voltage derived from the summingamplifier 84, is applied to the negative section via lines 230 and 262to diode 238 and to the positive segment of the switching circuit vialines 230 and 228 to diode 204. Thus, for positive values of 0,, thenegative segments are inhibited and for negative values of 0,, thepositive segments are inhibited.

In considering the operation of the circuit of FIG. 4, the upper portionof the circuit including the vector summer 12, dividers l4 and 16, andinverters 18, 20, 22 and 24 provide means for receiving X and Y inputsand for providing output voltages corresponding to the angular functionsshown in FIG. 3. The lower portion of FIG. 4 is the switching andsummation means for cumulatively summing in a positive or negativedirection voltages corresponding to the angular summation quantities.The quantities are stored and held at the switch points i and i1 35. Asthe angle is increased the newly generated quantities are added to thepreviously held quantities. These quantities are voltages representativeof functions of X, Y and R which correspond to angles dependent upon thevalue and polarity of X, Y and R.

To demonstrate the above, Y/R represents the angle 0 between i45 (seeFIG. 3). At +45, Y/R will hold its value as a clamped voltage limit (theeffect of the first clamping circuit) and the function 45 Y/R is zero.As the angle 0 increases, the value of 45 X/R will increase and is added(by the second clamping circuit) to the held, i.e., clamped, value ofY/R established by the first clamping circuit. At'135" the function 45X/R will equal 90 and .will be held at that value by the clamping effectof the second clamping circuit. Beyond the 135 angle the voltage valueof function 45 Y/R will be added to the previous held valuescorresponding respectively to the 45 angle Y/R limit and the 90 angle 45X/R limit. The 45 Y/R and 45 Y/R' value must be multiplied by two tocompensate for the decreasing Y/R value which had been stored in thefirst segment and which decreases in value between +135 and +180.

The diode bridge 102 has the voltages representing i45 across the bridgeas shown. The input is a voltage corresponding to the angle representedby Y/R and the output on line 130 will therefore be Y/R within the :45limits, at which limits its value will be held, i.e. clamped, until Y/Rbecomes less than the limit value. Diode bridge 102 and its associatedcomponents represents the first and fourth clamping circuits, the firstfor clamping at +45 and the fourth for 45 clamping.

The remaining clamping circuits, i.e., the second and third and thefifth and sixth, are all similar and will only pass the lower value ofits inputs and will block any signal of the wrong polarity. For example,considering the second clamping circuit which involves the diodes 144,166 and 168 and which has an input function of 45 X/R, this circuitcovers the angular segment of +45 to +135. In considering the operationof this second clamping circuit let us assume that the angle 0 isbetween +0 and +45. Under this condition thev voltage corresponding tothe function 45 X/R will be'a negative value and will be shorted throughits diode 166 but blocked by diode 144 preceding the summing resistor146 because the negative voltage is applied to the anode of the diode144. The voltage at the junction of the three diodes 144, 166 and 168will be equal to 45 X/R value minus the diode drop. The negative voltageat the junction of the diodes will reverse bias the diode 168 in serieswith the 90 angle voltage source constant in the segment +45 to +90",making it ineffective. Thus, the input to the summing amplifier 84 fromthe second clamping circuit, under the condition of Y/R being equal toor less than +45, is zero.

Consider now the operation of the same second circuit for an anglebeyond +45. Beyond +45 the function 45 Y/R becomes positive, the anodeof diode 144 is not negatively biased and it will conduct current fromthe reference voltage source indicated to the summing amplifier 84 toadd to the clamped voltage input from the first clamping circuit. Thevoltage at the junction of the diodes 144, 166. and 168 will be clampedat the voltage value of the function 45 X/R value'plus the diode voltagedrop. The diode 168 in series with the 90 constantvoltagewill bereversed biased until X/R 45, making the X/R -45 90and clamping thesegment, +45 to +l35, to a 90 value voltage. Thus, at +135 we have thesum of the clamped values of Y/R and 45 X/R.

Considering the operation of the third clamping circuit including thediodes 198, 200, 202 and 204, the input functional voltage is a voltagecorresponding to 45 Y/R. However, for the angular ranges of 0 to +45 and+45 to +l3 5 the input X/R is a negative value which applied to theanode side of diode 198 biases the diode to inoperative condition andthe output of the circuit is zero. In the angular range of to +225, thepolarity of X/R is positive and the blocking negative bias on diode 198is removed. I-Iowever, ambiguity may exist in the quadrant between +1 35and 135. This may be overcome by utilizing the polarity of Y or Y/R toinsure the correct variable will be introduced at the respective switchpoints +135 and 1 35. Inthe third and sixth circuits of FIG. 4, thevoltage output of angle 0, is taken from the output of summing amplifier84 and applied as inputs to the respective: diodes 238 of the negativesixth circuit and 204 of the positive angle third circuit. Thus, forpositive values of 0,, the negative segment, i.e., circuitsix, isinhibited because diode 198 would be negatively biased to inoperative vcondition and there would be zero output from the third circuit.

One further point about the third and sixth circuits is that the 45 Y/Rand the 45 Y/R values must be multiplied by two to compensate for thedecreasing Y/R value which had been stored in the first segment, Y/R,and decreases in value between +135 and 180. This is accomplished in thecircuit of FIG. 4 by making the value of resistors 208 and 252respectively of the third and sixth circuits each one-half of the valueof the corresponding resistors 1 32, 146 and 162 in. the first andsecond and fourth and fifth circuits.

Referring to FIG. 1, it will be noted that the computed angle willalways be smaller than the actual angle because the area of thetriangle, OAB, will always be less than the segment OACB area. Thiserror can be reduced by using-a conversion factor somewhat greater than573 in the conversion from radians to degrees. In the preferredembodiment of the invention, FIG. 4, this conversion factor iscontrolled by the potentiometer 96'on the operational amplifier 92. Asystem built as shown inFIG. 4 had a maximum error of i 1 over the $180range. To' obtain increased accuracy the number. of break points can beincreased With break points every 22.5 degrees, the theoretical accuracyis better, than ill) minutes.

What is claimed is: 1 1. A polarresolver for providing an analog voltagerepresentative of the angle corresponding to any the outputs of saiddivider and inverter means to provide a summation analog voltagerepresentative of the angle 0 to which said X and Y voltage inputscorrespond.

2. Apparatus according to claim 1, said summing and switching meansincluding:

summing amplifier means for providing the sum of first, second, twice athird, fourth, fifth and twice I a sixth inputs thereto from saiddivider and inverter means and corresponding respectively to the rangesof 0 to 45, 45 to 135, 135 to 225, -0 to 45, 45 tol35 and ,l35 to 225;

a first diode clamping circuit responsive to an operating input voltageof Y/R and a clamping voltage corresponding to 45 to provide said firstinput to said summing amplifier means;

a second diode clamping circuit responsive to an operating input voltageof 45 X/R, a clamping voltage of and an ambiguity resolving voltage toprovide said second input to said summing amplifier means;

a third diode clamping circuit responsive to an operating input voltageof Y/R, and an ambiguity resolving voltage to provide said third inputto said summing amplifier means;

a fourth diode clamping circuit responsive to an operating input voltageof Y/R, and a clamping voltage of 45 to provide said fourth input tosaid summing amplifier means; i

a fifth diode clamping circuit responsive to an operating input voltageof X/R 45, a clamping voltage of -90", and an ambiguity resolvingvoltage to provide said fifth input to said summing amplifier means; I

a sixth diode clamping circuit responsive to an operating input voltageof X/R, a clamping voltage of Y/R 45, and an ambiguity resolvingvoltage;

. inverter means,'responsive to'the output of said summing amplifiermeans,for providing said ambiguity resolving voltages; and

operational amplifier means, responsive to the output of said summingamplifier means and comprising an'adjustable attenuator feedback, forproviding a scaled output of the desired analog voltage correspondingtothe an e. 0. l

1. A polar resolver for providing an analog voltage representative ofthe angle theta corresponding to any given X and Y coordinates providedas X and Y voltage inputs, said resolver comprising: vector summer meansfor receiving said X and Y input voltages and providing correspondingvector radius R voltage outputs; divider means and inverter meansresponsive to said X and Y inputs for providing output voltages whichare functions of X, Y and R, each function representative of particularprogressive angular accretions of angle theta ; voltage switching andsumming means responsive to the outputs of said divider and invertermeans to provide a summation analog voltage representative of the angletheta to which said X and Y voltage inputs correspond.
 2. Apparatusaccording to claim 1, said summing and switching means including:summing amplifier means for providing the sum of first, second, twice athird, fourth, fifth and twice a sixth inputs thereto from said dividerand inverter means and corresponding respectively to the ranges of 0* to45*, 45* to 135*, 135* to 225*, -0* to -45*, -45* to -135* and -135* to-225*; a first diode clamping circuit responsive to an operating inputvoltage of Y/R and a clamping voltage corresponding to 45* to providesaid first input to said summing amplifier means; a second diodeclamping circuit responsive to an operating input voltage of 45* - X/R,a clamping voltage of 90*, and an ambiguity resolving voltage to providesaid second input to said summing amplifier means; a third diodeclamping circuit responsive to an operating input voltage of - Y/R, andan ambiguity resolving voltage to provide said third input to saidsumming amplifier means; a fourth diode clamping circuit responsive toan operating input voltage of Y/R, and a clamping voltage of -45* toprovide said fourth input to said summing amplifier means; a fifth diodeclamping circuit responsive to an operating input voltage of X/R - 45*,a clamping voltage of -90*, and an ambiguity resolving voltage toprovide said fifth input to said summing amplifier Means; a sixth diodeclamping circuit responsive to an operating input voltage of X/R, aclamping voltage of -Y/R -45*, and an ambiguity resolving voltage;inverter means, responsive to the output of said summing amplifiermeans, for providing said ambiguity resolving voltages; and operationalamplifier means, responsive to the output of said summing amplifiermeans and comprising an adjustable attenuator feedback, for providing ascaled output of the desired analog voltage corresponding to the angletheta .